Vascular rings, congenital intracardic anomalies of the aortic arch and the vessels emerging from the heart, completely encircle the trachea and esophagus [1]. The vascular ring results in narrowing and obstruction of the trachea and the esophagus. Due to the existence of a complete or partial vascular ring compressing either the trachea or esophagus, symptoms of a vascular ring in children include cough, stridor, chronic cough, dysphagia, persistent wheeze, and noisy breathing [2]. Some studies reported that the vascular ring surgery provides an excellent chance to improve the patient respiration conditions, especially for relief of symptoms [1–3]. Al-Bassam et al. reported that the thoracoscopic division of vascular rings in infants and children is a safe and effective surgery rather than an open thoracotomy[4]. Even after the treatment of a surgical division of the vascular ring, however, the fixed obstruction is relieved but the patient continues to have dynamic collapse because the compressed trachea segment is always malacic. Airway resistance to flow in the airway, thus, is a key factor for not only clinical diagnosis severity assessment but also therapeutic decision in tracheal stenosis. Furthermore, Malvè et al. (2011) utilized the finite element-based commercial software code (ADINA R&D Inc.) to model the fluid structure interaction of a human trachea under different ventilation conditions [5]. They also found that the positive pressure in the trachea does not result in the airway collapse during the time period of mechanical breathing. Therefore, the purpose of this study is to use the computational fluid dynamics (CFD) technique to calculate the local pressure drops in the tracheal segment for different inspiratory and expiratory flow rates due to preoperative and preoperative vascular ring surgery.

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